I. Field of the Invention
The present invention relates to inductors and, more particularly, to a tunable inductor.
II. Description of Relevant Art
Tunable inductors, and in particular MEMS tunable inductors, form an important component of both power and communication systems. Tunable inductors are used as a frequency control element in communication systems, allowing communication networks to be used in different frequency bands. Variable inductors can be used to vary the resonant frequency of inductor-capacitor (LC) tanks used in voltage controlled oscillators and other RF circuits and to control bandwidth and cut-off frequency of tunable filters. In power systems, tunable inductors can change the impedance of matching networks during operation, allowing load matching for more efficient power delivery.
There have been previously known MEMS tunable inductors which utilize actuators, such as electrostatic actuators, to vary the inductance of the inductor. A survey of the forms of MEMS tunable inductors commonly used is given in M. M. Teymoori and J. M. Ahangarkolaei, “MEMS tunable inductors: a survey,” Australian Journal of Basic and Applied Sciences, vol. 5, 2011, pp. 1868-1878, herein incorporated by reference. To briefly summarize, the largest tuning ratios are typically achieved using switch-based techniques, where the configuration of discrete inductors is changed, by for instance adding additional inductors in series by closing MEMS switches. Although effective, this technique only allows only a handful of specific inductance to be obtained; continuous tuning is impossible without an infinite number of segments and switches. A number of approaches have been demonstrated for creating continuous tuning, but typically with much smaller tuning ratios. These methods include changing the permeability of a magnetic material in the core by an additional bias field, or physically changing the position of coils relative to each other to change the coupling between them. A magnetic core can also be selectively inserted or retracted into a coil to change the inductance. As discussed in the survey paper, the best continuous tuning techniques available generally only can obtain a tuning ratio of 3 or 4.
The inductance of an inductor is dependent upon the strength and scale of the magnetic field that is created when electrical current passes through one or more inductors wound around the core. Consequently, inductors with magnetic cores of high permeability, such as iron-containing alloys or ceramics, are oftentimes used to increase the magnetic field response of the inductor. For a magnetic core inductor where the magnetic flux is contained within the core, the inductance L is given by
      L    =                            N          2                ⁢                  μ                      r            ,            core                          ⁢                  μ          0                ⁢                  A          core                            l        core              ,where N is the number of turns, lcore is the length of the loop, Acore is the core cross sectional area, μr,core is the relative permeability of the core and μ0 is the permeability of free space.
As shown, when the magnetic core fully links all of the inductor coils through a closed loop, the inductance is directly proportional to the permeability of the core. For example, common core materials such as iron-containing alloys or ceramics have permeabilities in the hundreds or thousands while some exotic materials, such as metglas, exhibit permeability in the millions. However, for high currents, most magnetic materials begin to saturate thus reaching a maximum magnetic flux density above which the inductor behaves nonlinearly.
In order to prevent saturation of the magnetic core, many magnetic cores include an air gap. With an air gap, the inductance of the coil is dominated by the air gap when μr,core is large; the inductance is approximately given by
      L    =                            N          2                                                                                                    l                gap                                                              μ                  0                                ⁢                                  A                  gap                                                      +                                          l                core                                                              μ                                      r                    ,                    core                                                  ⁢                                  μ                  0                                ⁢                                  A                  core                                                                        ≈                                    N            2                    ⁢                      μ            0                    ⁢                      A            gap                                    l          gap                      ,where Agap is the area of the gap and lgap is the length of the gap. Consequently, by providing an air gap, the linearity of the inductor is improved but at a great loss in the overall inductance of the inductor.